/*
 * @(#)CubicCurve2D.java	1.29 03/12/19
 *
 * Copyright 2004 Sun Microsystems, Inc. All rights reserved.
 * SUN PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
 */

package com.davetrudes.jung.client.graphics.geom;

import java.util.Arrays;

import com.davetrudes.jung.client.graphics.Rectangle;
import com.davetrudes.jung.client.graphics.Shape;

/**
 * The <code>CubicCurve2D</code> class defines a cubic parametric curve segment
 * in (x,&nbsp; y) coordinate space.
 * <p>
 * This class is only the abstract superclass for all objects which store a 2D
 * cubic curve segment. The actual storage representation of the coordinates is
 * left to the subclass.
 *
 * @version 1.29, 12/19/03
 * @author Jim Graham
 */
public abstract class CubicCurve2D implements Shape, Cloneable {
	/**
	 * A cubic parametric curve segment specified with double coordinates.
	 */
	public static class Double extends CubicCurve2D {
		/**
		 * The X coordinate of the start point of the cubic curve segment.
		 */
		public double x1;

		/**
		 * The Y coordinate of the start point of the cubic curve segment.
		 */
		public double y1;

		/**
		 * The X coordinate of the first control point of the cubic curve
		 * segment.
		 */
		public double ctrlx1;

		/**
		 * The Y coordinate of the first control point of the cubic curve
		 * segment.
		 */
		public double ctrly1;

		/**
		 * The X coordinate of the second control point of the cubic curve
		 * segment.
		 */
		public double ctrlx2;

		/**
		 * The Y coordinate of the second control point of the cubic curve
		 * segment.
		 */
		public double ctrly2;

		/**
		 * The X coordinate of the end point of the cubic curve segment.
		 */
		public double x2;

		/**
		 * The Y coordinate of the end point of the cubic curve segment.
		 */
		public double y2;

		/**
		 * Constructs and initializes a CubicCurve with coordinates (0, 0, 0, 0,
		 * 0, 0).
		 */
		public Double() {
		}

		/**
		 * Constructs and initializes a <code>CubicCurve2D</code> from the
		 * specified coordinates.
		 *
		 * @param x1
		 *            ,&nbsp;y1 the first specified coordinates for the start
		 *            point of the resulting <code>CubicCurve2D</code>
		 * @param ctrlx1
		 *            ,&nbsp;ctrly1 the second specified coordinates for the
		 *            first control point of the resulting
		 *            <code>CubicCurve2D</code>
		 * @param ctrlx2
		 *            ,&nbsp;ctrly2 the third specified coordinates for the
		 *            second control point of the resulting
		 *            <code>CubicCurve2D</code>
		 * @param x2
		 *            ,&nbsp;y2 the fourth specified coordinates for the end
		 *            point of the resulting <code>CubicCurve2D</code>
		 */
		public Double(double x1, double y1, double ctrlx1, double ctrly1,
				double ctrlx2, double ctrly2, double x2, double y2) {
			setCurve(x1, y1, ctrlx1, ctrly1, ctrlx2, ctrly2, x2, y2);
		}

		/**
		 * Returns the bounding box of the shape.
		 *
		 * @return a <code>Rectangle2D</code> that is the bounding box of the
		 *         shape.
		 */
		public Rectangle2D getBounds2D() {
			double left = Math.min(Math.min(x1, x2), Math.min(ctrlx1, ctrlx2));
			double top = Math.min(Math.min(y1, y2), Math.min(ctrly1, ctrly2));
			double right = Math.max(Math.max(x1, x2), Math.max(ctrlx1, ctrlx2));
			double bottom = Math
					.max(Math.max(y1, y2), Math.max(ctrly1, ctrly2));
			return new Rectangle2D.Double(left, top, right - left, bottom - top);
		}

		/**
		 * Returns the first control point.
		 *
		 * @return a <code>Point2D</code> that is the first control point of the
		 *         <code>CubicCurve2D</code>.
		 */
		public Point2D getCtrlP1() {
			return new Point2D.Double(ctrlx1, ctrly1);
		}

		/**
		 * Returns the second control point.
		 *
		 * @return a <code>Point2D</code> that is the second control point of
		 *         the <code>CubicCurve2D</code>.
		 */
		public Point2D getCtrlP2() {
			return new Point2D.Double(ctrlx2, ctrly2);
		}

		/**
		 * Returns the X coordinate of the first control point in double
		 * precision.
		 *
		 * @return the X coordinate of the first control point of the
		 *         <code>CubicCurve2D</code>.
		 */
		public double getCtrlX1() {
			return ctrlx1;
		}

		/**
		 * Returns the X coordinate of the second control point in double
		 * precision.
		 *
		 * @return the X coordinate of the second control point of the
		 *         <code>CubicCurve2D</code>.
		 */
		public double getCtrlX2() {
			return ctrlx2;
		}

		/**
		 * Returns the Y coordinate of the first control point in double
		 * precision.
		 *
		 * @return the Y coordinate of the first control point of the
		 *         <code>CubicCurve2D</code>.
		 */
		public double getCtrlY1() {
			return ctrly1;
		}

		/**
		 * Returns the Y coordinate of the second control point in double
		 * precision.
		 *
		 * @return the Y coordinate of the second control point of the
		 *         <code>CubicCurve2D</code>.
		 */
		public double getCtrlY2() {
			return ctrly2;
		}

		/**
		 * Returns the start point.
		 *
		 * @return a <code>Point2D</code> that is the start point of the
		 *         <code>CubicCurve2D</code>.
		 */
		public Point2D getP1() {
			return new Point2D.Double(x1, y1);
		}

		/**
		 * Returns the end point.
		 *
		 * @return a <code>Point2D</code> that is the end point of the
		 *         <code>CubicCurve2D</code>.
		 */
		public Point2D getP2() {
			return new Point2D.Double(x2, y2);
		}

		/**
		 * Returns the X coordinate of the start point in double precision.
		 *
		 * @return the X coordinate of the first control point of the
		 *         <code>CubicCurve2D</code>.
		 */
		public double getX1() {
			return x1;
		}

		/**
		 * Returns the X coordinate of the end point in double precision.
		 *
		 * @return the X coordinate of the end point of the
		 *         <code>CubicCurve2D</code>.
		 */
		public double getX2() {
			return x2;
		}

		/**
		 * Returns the Y coordinate of the start point in double precision.
		 *
		 * @return the Y coordinate of the start point of the
		 *         <code>CubicCurve2D</code>.
		 */
		public double getY1() {
			return y1;
		}

		/**
		 * Returns the Y coordinate of the end point in double precision.
		 *
		 * @return the Y coordinate of the end point of the
		 *         <code>CubicCurve2D</code>.
		 */
		public double getY2() {
			return y2;
		}

		/**
		 * Sets the location of the endpoints and controlpoints of this curve to
		 * the specified double coordinates.
		 *
		 * @param x1
		 *            ,&nbsp;y1 the first specified coordinates used to set the
		 *            start point of this <code>CubicCurve2D</code>
		 * @param ctrlx1
		 *            ,&nbsp;ctrly1 the second specified coordinates used to set
		 *            the first control point of this <code>CubicCurve2D</code>
		 * @param ctrlx2
		 *            ,&nbsp;ctrly2 the third specified coordinates used to set
		 *            the second control point of this <code>CubicCurve2D</code>
		 * @param x2
		 *            ,&nbsp;y2 the fourth specified coordinates used to set the
		 *            end point of this <code>CubicCurve2D</code>
		 */
		public void setCurve(double x1, double y1, double ctrlx1,
				double ctrly1, double ctrlx2, double ctrly2, double x2,
				double y2) {
			this.x1 = x1;
			this.y1 = y1;
			this.ctrlx1 = ctrlx1;
			this.ctrly1 = ctrly1;
			this.ctrlx2 = ctrlx2;
			this.ctrly2 = ctrly2;
			this.x2 = x2;
			this.y2 = y2;
		}
	}

	/**
	 * A cubic parametric curve segment specified with float coordinates.
	 */
	public static class Float extends CubicCurve2D {
		/**
		 * The X coordinate of the start point of the cubic curve segment.
		 */
		public float x1;

		/**
		 * The Y coordinate of the start point of the cubic curve segment.
		 */
		public float y1;

		/**
		 * The X coordinate of the first control point of the cubic curve
		 * segment.
		 */
		public float ctrlx1;

		/**
		 * The Y coordinate of the first control point of the cubic curve
		 * segment.
		 */
		public float ctrly1;

		/**
		 * The X coordinate of the second control point of the cubic curve
		 * segment.
		 */
		public float ctrlx2;

		/**
		 * The Y coordinate of the second control point of the cubic curve
		 * segment.
		 */
		public float ctrly2;

		/**
		 * The X coordinate of the end point of the cubic curve segment.
		 */
		public float x2;

		/**
		 * The Y coordinate of the end point of the cubic curve segment.
		 */
		public float y2;

		/**
		 * Constructs and initializes a CubicCurve with coordinates (0, 0, 0, 0,
		 * 0, 0).
		 */
		public Float() {
		}

		/**
		 * Constructs and initializes a <code>CubicCurve2D</code> from the
		 * specified coordinates.
		 *
		 * @param x1
		 *            ,&nbsp;y1 the first specified coordinates for the start
		 *            point of the resulting <code>CubicCurve2D</code>
		 * @param ctrlx1
		 *            ,&nbsp;ctrly1 the second specified coordinates for the
		 *            first control point of the resulting
		 *            <code>CubicCurve2D</code>
		 * @param ctrlx2
		 *            ,&nbsp;ctrly2 the third specified coordinates for the
		 *            second control point of the resulting
		 *            <code>CubicCurve2D</code>
		 * @param x2
		 *            ,&nbsp;y2 the fourth specified coordinates for the end
		 *            point of the resulting <code>CubicCurve2D</code>
		 */
		public Float(float x1, float y1, float ctrlx1, float ctrly1,
				float ctrlx2, float ctrly2, float x2, float y2) {
			setCurve(x1, y1, ctrlx1, ctrly1, ctrlx2, ctrly2, x2, y2);
		}

		/**
		 * Returns the bounding box of the shape.
		 *
		 * @return a {@link Rectangle2D} that is the bounding box of the shape.
		 */
		public Rectangle2D getBounds2D() {
			float left = Math.min(Math.min(x1, x2), Math.min(ctrlx1, ctrlx2));
			float top = Math.min(Math.min(y1, y2), Math.min(ctrly1, ctrly2));
			float right = Math.max(Math.max(x1, x2), Math.max(ctrlx1, ctrlx2));
			float bottom = Math.max(Math.max(y1, y2), Math.max(ctrly1, ctrly2));
			return new Rectangle2D.Float(left, top, right - left, bottom - top);
		}

		/**
		 * Returns the first control point.
		 *
		 * @return a <code>Point2D</code> that is the first control point of the
		 *         <code>CubicCurve2D</code>.
		 */
		public Point2D getCtrlP1() {
			return new Point2D.Float(ctrlx1, ctrly1);
		}

		/**
		 * Returns the second control point.
		 *
		 * @return a <code>Point2D</code> that is the second control point of
		 *         the <code>CubicCurve2D</code>.
		 */
		public Point2D getCtrlP2() {
			return new Point2D.Float(ctrlx2, ctrly2);
		}

		/**
		 * Returns the X coordinate of the first control point in double
		 * precision.
		 *
		 * @return the X coordinate of the first control point of the
		 *         <code>CubicCurve2D</code>.
		 */
		public double getCtrlX1() {
			return (double) ctrlx1;
		}

		/**
		 * Returns the X coordinate of the second control point in double
		 * precision.
		 *
		 * @return the X coordinate of the second control point of the
		 *         <code>CubicCurve2D</code>.
		 */
		public double getCtrlX2() {
			return (double) ctrlx2;
		}

		/**
		 * Returns the Y coordinate of the first control point in double
		 * precision.
		 *
		 * @return the Y coordinate of the first control point of the
		 *         <code>CubicCurve2D</code>.
		 */
		public double getCtrlY1() {
			return (double) ctrly1;
		}

		/**
		 * Returns the Y coordinate of the second control point in double
		 * precision.
		 *
		 * @return the Y coordinate of the second control point of the
		 *         <code>CubicCurve2D</code>.
		 */
		public double getCtrlY2() {
			return (double) ctrly2;
		}

		/**
		 * Returns the start point.
		 *
		 * @return a {@link Point2D} that is the start point of the
		 *         <code>CubicCurve2D</code>.
		 */
		public Point2D getP1() {
			return new Point2D.Float(x1, y1);
		}

		/**
		 * Returns the end point.
		 *
		 * @return a <code>Point2D</code> that is the end point of the
		 *         <code>CubicCurve2D</code>.
		 */
		public Point2D getP2() {
			return new Point2D.Float(x2, y2);
		}

		/**
		 * Returns the X coordinate of the start point in double precision.
		 *
		 * @return the X coordinate of the start point of the
		 *         <code>CubicCurve2D</code>.
		 */
		public double getX1() {
			return (double) x1;
		}

		/**
		 * Returns the X coordinate of the end point in double precision.
		 *
		 * @return the X coordinate of the end point of the
		 *         <code>CubicCurve2D</code>.
		 */
		public double getX2() {
			return (double) x2;
		}

		/**
		 * Returns the Y coordinate of the start point in double precision.
		 *
		 * @return the Y coordinate of the start point of the
		 *         <code>CubicCurve2D</code>.
		 */
		public double getY1() {
			return (double) y1;
		}

		/**
		 * Returns the Y coordinate of the end point in double precision.
		 *
		 * @return the Y coordinate of the end point of the
		 *         <code>CubicCurve2D</code>.
		 */
		public double getY2() {
			return (double) y2;
		}

		/**
		 * Sets the location of the endpoints and controlpoints of this
		 * <code>CubicCurve2D</code> to the specified double coordinates.
		 *
		 * @param x1
		 *            ,&nbsp;y1 the first specified coordinates used to set the
		 *            start point of this <code>CubicCurve2D</code>
		 * @param ctrlx1
		 *            ,&nbsp;ctrly1 the second specified coordinates used to set
		 *            the first control point of this <code>CubicCurve2D</code>
		 * @param ctrlx2
		 *            ,&nbsp;ctrly2 the third specified coordinates used to set
		 *            the second control point of this <code>CubicCurve2D</code>
		 * @param x2
		 *            ,&nbsp;y2 the fourth specified coordinates used to set the
		 *            end point of this <code>CubicCurve2D</code>
		 */
		public void setCurve(double x1, double y1, double ctrlx1,
				double ctrly1, double ctrlx2, double ctrly2, double x2,
				double y2) {
			this.x1 = (float) x1;
			this.y1 = (float) y1;
			this.ctrlx1 = (float) ctrlx1;
			this.ctrly1 = (float) ctrly1;
			this.ctrlx2 = (float) ctrlx2;
			this.ctrly2 = (float) ctrly2;
			this.x2 = (float) x2;
			this.y2 = (float) y2;
		}

		/**
		 * Sets the location of the endpoints and controlpoints of this curve to
		 * the specified float coordinates.
		 *
		 * @param x1
		 *            ,&nbsp;y1 the first specified coordinates used to set the
		 *            start point of this <code>CubicCurve2D</code>
		 * @param ctrlx1
		 *            ,&nbsp;ctrly1 the second specified coordinates used to set
		 *            the first control point of this <code>CubicCurve2D</code>
		 * @param ctrlx2
		 *            ,&nbsp;ctrly2 the third specified coordinates used to set
		 *            the second control point of this <code>CubicCurve2D</code>
		 * @param x2
		 *            ,&nbsp;y2 the fourth specified coordinates used to set the
		 *            end point of this <code>CubicCurve2D</code>
		 */
		public void setCurve(float x1, float y1, float ctrlx1, float ctrly1,
				float ctrlx2, float ctrly2, float x2, float y2) {
			this.x1 = x1;
			this.y1 = y1;
			this.ctrlx1 = ctrlx1;
			this.ctrly1 = ctrly1;
			this.ctrlx2 = ctrlx2;
			this.ctrly2 = ctrly2;
			this.x2 = x2;
			this.y2 = y2;
		}
	}

	private static final int BELOW = -2;

	private static final int LOWEDGE = -1;

	private static final int INSIDE = 0;

	private static final int HIGHEDGE = 1;

	private static final int ABOVE = 2;

	/**
	 * Returns the flatness of the cubic curve specified by the indicated
	 * controlpoints. The flatness is the maximum distance of a controlpoint
	 * from the line connecting the endpoints.
	 *
	 * @param x1
	 *            ,&nbsp;y1 the first specified coordinates that specify the
	 *            start point of a <code>CubicCurve2D</code>
	 * @param ctrlx1
	 *            ,&nbsp;ctrly1 the second specified coordinates that specify
	 *            the first control point of a <code>CubicCurve2D</code>
	 * @param ctrlx2
	 *            ,&nbsp;ctrly2 the third specified coordinates that specify the
	 *            second control point of a <code>CubicCurve2D</code>
	 * @param x2
	 *            ,&nbsp;y2 the fourth specified coordinates that specify the
	 *            end point of a <code>CubicCurve2D</code>
	 * @return the flatness of the <code>CubicCurve2D</code> represented by the
	 *         specified coordinates.
	 */
	public static double getFlatness(double x1, double y1, double ctrlx1,
			double ctrly1, double ctrlx2, double ctrly2, double x2, double y2) {
		return Math.sqrt(getFlatnessSq(x1, y1, ctrlx1, ctrly1, ctrlx2, ctrly2,
				x2, y2));
	}

	/**
	 * Returns the flatness of the cubic curve specified by the controlpoints
	 * stored in the indicated array at the indicated index. The flatness is the
	 * maximum distance of a controlpoint from the line connecting the
	 * endpoints.
	 *
	 * @param coords
	 *            an array containing coordinates
	 * @param offset
	 *            the index of <code>coords</code> at which to begin setting the
	 *            endpoints and controlpoints of this curve to the coordinates
	 *            contained in <code>coords</code>
	 * @return the flatness of the <code>CubicCurve2D</code> specified by the
	 *         coordinates in <code>coords</code> at the specified offset.
	 */
	public static double getFlatness(double coords[], int offset) {
		return getFlatness(coords[offset + 0], coords[offset + 1],
				coords[offset + 2], coords[offset + 3], coords[offset + 4],
				coords[offset + 5], coords[offset + 6], coords[offset + 7]);
	}

	/**
	 * Returns the square of the flatness of the cubic curve specified by the
	 * indicated controlpoints. The flatness is the maximum distance of a
	 * controlpoint from the line connecting the endpoints.
	 *
	 * @param x1
	 *            ,&nbsp;y1 the first specified coordinates that specify the
	 *            start point of a <code>CubicCurve2D</code>
	 * @param ctrlx1
	 *            ,&nbsp;ctrly1 the second specified coordinates that specify
	 *            the first control point of a <code>CubicCurve2D</code>
	 * @param ctrlx2
	 *            ,&nbsp;ctrly2 the third specified coordinates that specify the
	 *            second control point of a <code>CubicCurve2D</code>
	 * @param x2
	 *            ,&nbsp;y2 the fourth specified coordinates that specify the
	 *            end point of a <code>CubicCurve2D</code>
	 * @return the square of the flatness of the <code>CubicCurve2D</code>
	 *         represented by the specified coordinates.
	 */
	public static double getFlatnessSq(double x1, double y1, double ctrlx1,
			double ctrly1, double ctrlx2, double ctrly2, double x2, double y2) {
		return Math.max(Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx1, ctrly1),
				Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx2, ctrly2));

	}

	/**
	 * Returns the square of the flatness of the cubic curve specified by the
	 * controlpoints stored in the indicated array at the indicated index. The
	 * flatness is the maximum distance of a controlpoint from the line
	 * connecting the endpoints.
	 *
	 * @param coords
	 *            an array containing coordinates
	 * @param offset
	 *            the index of <code>coords</code> at which to begin setting the
	 *            endpoints and controlpoints of this curve to the coordinates
	 *            contained in <code>coords</code>
	 * @return the square of the flatness of the <code>CubicCurve2D</code>
	 *         specified by the coordinates in <code>coords</code> at the
	 *         specified offset.
	 */
	public static double getFlatnessSq(double coords[], int offset) {
		return getFlatnessSq(coords[offset + 0], coords[offset + 1],
				coords[offset + 2], coords[offset + 3], coords[offset + 4],
				coords[offset + 5], coords[offset + 6], coords[offset + 7]);
	}

	/**
	 * Solves the cubic whose coefficients are in the <code>eqn</code> array and
	 * places the non-complex roots back into the same array, returning the
	 * number of roots. The solved cubic is represented by the equation:
	 *
	 * <pre>
	 *     eqn = {c, b, a, d}
	 *     dx&circ;3 + ax&circ;2 + bx + c = 0
	 * </pre>
	 *
	 * A return value of -1 is used to distinguish a constant equation that
	 * might be always 0 or never 0 from an equation that has no zeroes.
	 *
	 * @param eqn
	 *            an array containing coefficients for a cubic
	 * @return the number of roots, or -1 if the equation is a constant.
	 */
	public static int solveCubic(double eqn[]) {
		return solveCubic(eqn, eqn);
	}

	/**
	 * Solve the cubic whose coefficients are in the <code>eqn</code> array and
	 * place the non-complex roots into the <code>res</code> array, returning
	 * the number of roots. The cubic solved is represented by the equation: eqn
	 * = {c, b, a, d} dx^3 + ax^2 + bx + c = 0 A return value of -1 is used to
	 * distinguish a constant equation, which may be always 0 or never 0, from
	 * an equation which has no zeroes.
	 *
	 * @param eqn
	 *            the specified array of coefficients to use to solve the cubic
	 *            equation
	 * @param res
	 *            the array that contains the non-complex roots resulting from
	 *            the solution of the cubic equation
	 * @return the number of roots, or -1 if the equation is a constant
	 */
	public static int solveCubic(double eqn[], double res[]) {
		// From Numerical Recipes, 5.6, Quadratic and Cubic Equations
		double d = eqn[3];
		if (d == 0.0) {
			// The cubic has degenerated to quadratic (or line or ...).
			return QuadCurve2D.solveQuadratic(eqn, res);
		}
		double a = eqn[2] / d;
		double b = eqn[1] / d;
		double c = eqn[0] / d;
		int roots = 0;
		double Q = (a * a - 3.0 * b) / 9.0;
		double R = (2.0 * a * a * a - 9.0 * a * b + 27.0 * c) / 54.0;
		double R2 = R * R;
		double Q3 = Q * Q * Q;
		a = a / 3.0;
		if (R2 < Q3) {
			double theta = Math.acos(R / Math.sqrt(Q3));
			Q = -2.0 * Math.sqrt(Q);
			if (res == eqn) {
				// Copy the eqn so that we don't clobber it with the
				// roots. This is needed so that fixRoots can do its
				// work with the original equation.
				eqn = new double[4];
				System.arraycopy(res, 0, eqn, 0, 4);
			}
			res[roots++] = Q * Math.cos(theta / 3.0) - a;
			res[roots++] = Q * Math.cos((theta + Math.PI * 2.0) / 3.0) - a;
			res[roots++] = Q * Math.cos((theta - Math.PI * 2.0) / 3.0) - a;
			fixRoots(res, eqn);
		} else {
			boolean neg = (R < 0.0);
			double S = Math.sqrt(R2 - Q3);
			if (neg) {
				R = -R;
			}
			double A = Math.pow(R + S, 1.0 / 3.0);
			if (!neg) {
				A = -A;
			}
			double B = (A == 0.0) ? 0.0 : (Q / A);
			res[roots++] = (A + B) - a;
		}
		return roots;
	}

	/**
	 * Subdivides the cubic curve specified by the <code>src</code> parameter
	 * and stores the resulting two subdivided curves into the <code>left</code>
	 * and <code>right</code> curve parameters. Either or both of the
	 * <code>left</code> and <code>right</code> objects may be the same as the
	 * <code>src</code> object or <code>null</code>.
	 *
	 * @param src
	 *            the cubic curve to be subdivided
	 * @param left
	 *            the cubic curve object for storing the left or first half of
	 *            the subdivided curve
	 * @param right
	 *            the cubic curve object for storing the right or second half of
	 *            the subdivided curve
	 */
	public static void subdivide(CubicCurve2D src, CubicCurve2D left,
			CubicCurve2D right) {
		double x1 = src.getX1();
		double y1 = src.getY1();
		double ctrlx1 = src.getCtrlX1();
		double ctrly1 = src.getCtrlY1();
		double ctrlx2 = src.getCtrlX2();
		double ctrly2 = src.getCtrlY2();
		double x2 = src.getX2();
		double y2 = src.getY2();
		double centerx = (ctrlx1 + ctrlx2) / 2.0;
		double centery = (ctrly1 + ctrly2) / 2.0;
		ctrlx1 = (x1 + ctrlx1) / 2.0;
		ctrly1 = (y1 + ctrly1) / 2.0;
		ctrlx2 = (x2 + ctrlx2) / 2.0;
		ctrly2 = (y2 + ctrly2) / 2.0;
		double ctrlx12 = (ctrlx1 + centerx) / 2.0;
		double ctrly12 = (ctrly1 + centery) / 2.0;
		double ctrlx21 = (ctrlx2 + centerx) / 2.0;
		double ctrly21 = (ctrly2 + centery) / 2.0;
		centerx = (ctrlx12 + ctrlx21) / 2.0;
		centery = (ctrly12 + ctrly21) / 2.0;
		if (left != null) {
			left.setCurve(x1, y1, ctrlx1, ctrly1, ctrlx12, ctrly12, centerx,
					centery);
		}
		if (right != null) {
			right.setCurve(centerx, centery, ctrlx21, ctrly21, ctrlx2, ctrly2,
					x2, y2);
		}
	}

	/**
	 * Subdivides the cubic curve specified by the coordinates stored in the
	 * <code>src</code> array at indices <code>srcoff</code> through (
	 * <code>srcoff</code>&nbsp;+&nbsp;7) and stores the resulting two
	 * subdivided curves into the two result arrays at the corresponding
	 * indices. Either or both of the <code>left</code> and <code>right</code>
	 * arrays may be <code>null</code> or a reference to the same array as the
	 * <code>src</code> array. Note that the last point in the first subdivided
	 * curve is the same as the first point in the second subdivided curve.
	 * Thus, it is possible to pass the same array for <code>left</code> and
	 * <code>right</code> and to use offsets, such as <code>rightoff</code>
	 * equals (<code>leftoff</code> + 6), in order to avoid allocating extra
	 * storage for this common point.
	 *
	 * @param src
	 *            the array holding the coordinates for the source curve
	 * @param srcoff
	 *            the offset into the array of the beginning of the the 6 source
	 *            coordinates
	 * @param left
	 *            the array for storing the coordinates for the first half of
	 *            the subdivided curve
	 * @param leftoff
	 *            the offset into the array of the beginning of the the 6 left
	 *            coordinates
	 * @param right
	 *            the array for storing the coordinates for the second half of
	 *            the subdivided curve
	 * @param rightoff
	 *            the offset into the array of the beginning of the the 6 right
	 *            coordinates
	 */
	public static void subdivide(double src[], int srcoff, double left[],
			int leftoff, double right[], int rightoff) {
		double x1 = src[srcoff + 0];
		double y1 = src[srcoff + 1];
		double ctrlx1 = src[srcoff + 2];
		double ctrly1 = src[srcoff + 3];
		double ctrlx2 = src[srcoff + 4];
		double ctrly2 = src[srcoff + 5];
		double x2 = src[srcoff + 6];
		double y2 = src[srcoff + 7];
		if (left != null) {
			left[leftoff + 0] = x1;
			left[leftoff + 1] = y1;
		}
		if (right != null) {
			right[rightoff + 6] = x2;
			right[rightoff + 7] = y2;
		}
		x1 = (x1 + ctrlx1) / 2.0;
		y1 = (y1 + ctrly1) / 2.0;
		x2 = (x2 + ctrlx2) / 2.0;
		y2 = (y2 + ctrly2) / 2.0;
		double centerx = (ctrlx1 + ctrlx2) / 2.0;
		double centery = (ctrly1 + ctrly2) / 2.0;
		ctrlx1 = (x1 + centerx) / 2.0;
		ctrly1 = (y1 + centery) / 2.0;
		ctrlx2 = (x2 + centerx) / 2.0;
		ctrly2 = (y2 + centery) / 2.0;
		centerx = (ctrlx1 + ctrlx2) / 2.0;
		centery = (ctrly1 + ctrly2) / 2.0;
		if (left != null) {
			left[leftoff + 2] = x1;
			left[leftoff + 3] = y1;
			left[leftoff + 4] = ctrlx1;
			left[leftoff + 5] = ctrly1;
			left[leftoff + 6] = centerx;
			left[leftoff + 7] = centery;
		}
		if (right != null) {
			right[rightoff + 0] = centerx;
			right[rightoff + 1] = centery;
			right[rightoff + 2] = ctrlx2;
			right[rightoff + 3] = ctrly2;
			right[rightoff + 4] = x2;
			right[rightoff + 5] = y2;
		}
	}

	/*
	 * Evaluate the t values in the first num slots of the vals[] array and
	 * place the evaluated values back into the same array. Only evaluate t
	 * values that are within the range <0, 1>, including the 0 and 1 ends of
	 * the range iff the include0 or include1 booleans are true. If an
	 * "inflection" equation is handed in, then any points which represent a
	 * point of inflection for that cubic equation are also ignored.
	 */
	private static int evalCubic(double vals[], int num, boolean include0,
			boolean include1, double inflect[], double c1, double cp1,
			double cp2, double c2) {
		int j = 0;
		for (int i = 0; i < num; i++) {
			double t = vals[i];
			if ((include0 ? t >= 0 : t > 0)
					&& (include1 ? t <= 1 : t < 1)
					&& (inflect == null || inflect[1]
							+ (2 * inflect[2] + 3 * inflect[3] * t) * t != 0)) {
				double u = 1 - t;
				vals[j++] = c1 * u * u * u + 3 * cp1 * t * u * u + 3 * cp2 * t
						* t * u + c2 * t * t * t;
			}
		}
		return j;
	}

	/*
	 * Fill an array with the coefficients of the parametric equation in t,
	 * ready for solving against val with solveCubic. We currently have: val =
	 * P(t) = C1(1-t)^3 + 3CP1 t(1-t)^2 + 3CP2 t^2(1-t) + C2 t^3 = C1 - 3C1t +
	 * 3C1t^2 - C1t^3 + 3CP1t - 6CP1t^2 + 3CP1t^3 + 3CP2t^2 - 3CP2t^3 + C2t^3 0
	 * = (C1 - val) + (3CP1 - 3C1) t + (3C1 - 6CP1 + 3CP2) t^2 + (C2 - 3CP2 +
	 * 3CP1 - C1) t^3 0 = C + Bt + At^2 + Dt^3 C = C1 - val B = 3CP1 - 3C1 A =
	 * 3CP2 - 6CP1 + 3C1 D = C2 - 3CP2 + 3CP1 - C1
	 *
	 * @param x,&nbsp;y the coordinates of the upper left corner of the
	 * specified rectangular shape
	 *
	 * @param w the width of the specified rectangular shape
	 *
	 * @param h the height of the specified rectangular shape
	 *
	 * @return <code>true</code> if the shape intersects the interior of the the
	 * specified set of rectangular coordinates; <code>false</code> otherwise.
	 */
	private static void fillEqn(double eqn[], double val, double c1,
			double cp1, double cp2, double c2) {
		eqn[0] = c1 - val;
		eqn[1] = (cp1 - c1) * 3.0;
		eqn[2] = (cp2 - cp1 - cp1 + c1) * 3.0;
		eqn[3] = c2 + (cp1 - cp2) * 3.0 - c1;
		return;
	}

	private static double findZero(double t, double target, double eqn[]) {
		double slopeqn[] = { eqn[1], 2 * eqn[2], 3 * eqn[3] };
		double slope;
		double origdelta = 0;
		double origt = t;
		while (true) {
			slope = solveEqn(slopeqn, 2, t);
			if (slope == 0) {
				// At a local minima - must return
				return t;
			}
			double y = solveEqn(eqn, 3, t);
			if (y == 0) {
				// Found it! - return it
				return t;
			}
			// assert(slope != 0 && y != 0);
			double delta = -(y / slope);
			// assert(delta != 0);
			if (origdelta == 0) {
				origdelta = delta;
			}
			if (t < target) {
				if (delta < 0)
					return t;
			} else if (t > target) {
				if (delta > 0)
					return t;
			} else { /* t == target */
				return (delta > 0 ? (target + java.lang.Double.MIN_VALUE)
						: (target - java.lang.Double.MIN_VALUE));
			}
			double newt = t + delta;
			if (t == newt) {
				// The deltas are so small that we aren't moving...
				return t;
			}
			if (delta * origdelta < 0) {
				// We have reversed our path.
				int tag = (origt < t ? getTag(target, origt, t) : getTag(
						target, t, origt));
				if (tag != INSIDE) {
					// Local minima found away from target - return the middle
					return (origt + t) / 2;
				}
				// Local minima somewhere near target - move to target
				// and let the slope determine the resulting t.
				t = target;
			} else {
				t = newt;
			}
		}
	}

	/*
	 * This pruning step is necessary since solveCubic uses the cosine function
	 * to calculate the roots when there are 3 of them. Since the cosine method
	 * can have an error of +/- 1E-14 we need to make sure that we don't make
	 * any bad decisions due to an error.
	 *
	 * If the root is not near one of the endpoints, then we will only have a
	 * slight inaccuracy in calculating the x intercept which will only cause a
	 * slightly wrong answer for some points very close to the curve. While the
	 * results in that case are not as accurate as they could be, they are not
	 * disastrously inaccurate either.
	 *
	 * On the other hand, if the error happens near one end of the curve, then
	 * our processing to reject values outside of the t=[0,1] range will fail
	 * and the results of that failure will be disastrous since for an entire
	 * horizontal range of test points, we will either overcount or undercount
	 * the crossings and get a wrong answer for all of them, even when they are
	 * clearly and obviously inside or outside the curve.
	 *
	 * To work around this problem, we try a couple of Newton-Raphson iterations
	 * to see if the true root is closer to the endpoint or further away. If it
	 * is further away, then we can stop since we know we are on the right side
	 * of the endpoint. If we change direction, then either we are now being
	 * dragged away from the endpoint in which case the first condition will
	 * cause us to stop, or we have passed the endpoint and are headed back. In
	 * the second case, we simply evaluate the slope at the endpoint itself and
	 * place ourselves on the appropriate side of it or on it depending on that
	 * result.
	 */
	private static void fixRoots(double res[], double eqn[]) {
		final double EPSILON = 1E-5;
		for (int i = 0; i < 3; i++) {
			double t = res[i];
			if (Math.abs(t) < EPSILON) {
				res[i] = findZero(t, 0, eqn);
			} else if (Math.abs(t - 1) < EPSILON) {
				res[i] = findZero(t, 1, eqn);
			}
		}
	}

	/*
	 * Determine where coord lies with respect to the range from low to high. It
	 * is assumed that low <= high. The return value is one of the 5 values
	 * BELOW, LOWEDGE, INSIDE, HIGHEDGE, or ABOVE.
	 */
	private static int getTag(double coord, double low, double high) {
		if (coord <= low) {
			return (coord < low ? BELOW : LOWEDGE);
		}
		if (coord >= high) {
			return (coord > high ? ABOVE : HIGHEDGE);
		}
		return INSIDE;
	}

	/*
	 * Determine if the pttag represents a coordinate that is already in its
	 * test range, or is on the border with either of the two opttags
	 * representing another coordinate that is "towards the inside" of that test
	 * range. In other words, are either of the two "opt" points
	 * "drawing the pt inward"?
	 */
	private static boolean inwards(int pttag, int opt1tag, int opt2tag) {
		switch (pttag) {
		case BELOW:
		case ABOVE:
		default:
			return false;
		case LOWEDGE:
			return (opt1tag >= INSIDE || opt2tag >= INSIDE);
		case INSIDE:
			return true;
		case HIGHEDGE:
			return (opt1tag <= INSIDE || opt2tag <= INSIDE);
		}
	}

	private static double solveEqn(double eqn[], int order, double t) {
		double v = eqn[order];
		while (--order >= 0) {
			v = v * t + eqn[order];
		}
		return v;
	}

	/**
	 * This is an abstract class that cannot be instantiated directly.
	 * Type-specific implementation subclasses are available for instantiation
	 * and provide a number of formats for storing the information necessary to
	 * satisfy the various accessor methods below.
	 *
	 * @see java.awt.geom.CubicCurve2D.Float
	 * @see java.awt.geom.CubicCurve2D.Double
	 */
	protected CubicCurve2D() {
	}

	/**
	 * Tests if a specified coordinate is inside the boundary of the shape.
	 *
	 * @param x
	 *            ,&nbsp;y the specified coordinate to be tested
	 * @return <code>true</code> if the coordinate is inside the boundary of the
	 *         shape; <code>false</code> otherwise.
	 */
	public boolean contains(double x, double y) {
		// We count the "Y" crossings to determine if the point is
		// inside the curve bounded by its closing line.
		int crossings = 0;
		double x1 = getX1();
		double y1 = getY1();
		double x2 = getX2();
		double y2 = getY2();
		// First check for a crossing of the line connecting the endpoints
		double dy = y2 - y1;
		if ((dy > 0.0 && y >= y1 && y <= y2)
				|| (dy < 0.0 && y <= y1 && y >= y2)) {
			if (x < x1 + (y - y1) * (x2 - x1) / dy) {
				crossings++;
			}
		}
		// Solve the Y parametric equation for intersections with y
		double ctrlx1 = getCtrlX1();
		double ctrly1 = getCtrlY1();
		double ctrlx2 = getCtrlX2();
		double ctrly2 = getCtrlY2();
		boolean include0 = ((y2 - y1) * (ctrly1 - y1) >= 0);
		boolean include1 = ((y1 - y2) * (ctrly2 - y2) >= 0);
		double eqn[] = new double[4];
		double res[] = new double[4];
		fillEqn(eqn, y, y1, ctrly1, ctrly2, y2);
		int roots = solveCubic(eqn, res);
		roots = evalCubic(res, roots, include0, include1, eqn, x1, ctrlx1,
				ctrlx2, x2);
		while (--roots >= 0) {
			if (x < res[roots]) {
				crossings++;
			}
		}
		return ((crossings & 1) == 1);
	}

	/**
	 * Tests if the interior of the shape entirely contains the specified set of
	 * rectangular coordinates.
	 *
	 * @param x
	 *            ,&nbsp;y the coordinates of the upper left corner of the
	 *            specified rectangular shape
	 * @param w
	 *            the width of the specified rectangular shape
	 * @param h
	 *            the height of the specified rectangular shape
	 * @return <code>true</code> if the shape entirely contains the specified
	 *         set of rectangular coordinates; <code>false</code> otherwise.
	 */
	public boolean contains(double x, double y, double w, double h) {
		// Assertion: Cubic curves closed by connecting their
		// endpoints form either one or two convex halves with
		// the closing line segment as an edge of both sides.
		if (!(contains(x, y) && contains(x + w, y) && contains(x + w, y + h) && contains(
				x, y + h))) {
			return false;
		}
		// Either the rectangle is entirely inside one of the convex
		// halves or it crosses from one to the other, in which case
		// it must intersect the closing line segment.
		Rectangle2D rect = new Rectangle2D.Double(x, y, w, h);
		return !rect.intersectsLine(getX1(), getY1(), getX2(), getY2());
	}

	/**
	 * Tests if a specified <code>Point2D</code> is inside the boundary of the
	 * shape.
	 *
	 * @param p
	 *            the specified <code>Point2D</code> to be tested
	 * @return <code>true</code> if the <code>p</code> is inside the boundary of
	 *         the shape; <code>false</code> otherwise.
	 */
	public boolean contains(Point2D p) {
		return contains(p.getX(), p.getY());
	}

	/**
	 * Tests if the interior of the shape entirely contains the specified
	 * <code>Rectangle2D</code>.
	 *
	 * @param r
	 *            the specified <code>Rectangle2D</code> to be tested
	 * @return <code>true</code> if the shape entirely contains the specified
	 *         <code>Rectangle2D</code>; <code>false</code> otherwise.
	 */
	public boolean contains(Rectangle2D r) {
		return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight());
	}

	/**
	 * Returns the bounding box of the shape.
	 *
	 * @return a {@link Rectangle} that is the bounding box of the shape.
	 */
	public Rectangle getBounds() {
		return getBounds2D().getBounds();
	}

	/**
	 * Returns the first control point.
	 *
	 * @return a <code>Point2D</code> that is the first control point of the
	 *         <code>CubicCurve2D</code>.
	 */
	public abstract Point2D getCtrlP1();

	/**
	 * Returns the second control point.
	 *
	 * @return a <code>Point2D</code> that is the second control point of the
	 *         <code>CubicCurve2D</code>.
	 */
	public abstract Point2D getCtrlP2();

	/**
	 * Returns the X coordinate of the first control point in double precision.
	 *
	 * @return the X coordinate of the first control point of the
	 *         <code>CubicCurve2D</code>.
	 */
	public abstract double getCtrlX1();

	/**
	 * Returns the X coordinate of the second control point in double precision.
	 *
	 * @return the X coordinate of the second control point of the
	 *         <code>CubicCurve2D</code>.
	 */
	public abstract double getCtrlX2();

	/**
	 * Returns the Y coordinate of the first control point in double precision.
	 *
	 * @return the Y coordinate of the first control point of the
	 *         <code>CubicCurve2D</code>.
	 */
	public abstract double getCtrlY1();

	/**
	 * Returns the Y coordinate of the second control point in double precision.
	 *
	 * @return the Y coordinate of the second control point of the
	 *         <code>CubicCurve2D</code>.
	 */
	public abstract double getCtrlY2();

	/**
	 * Returns the flatness of this curve. The flatness is the maximum distance
	 * of a controlpoint from the line connecting the endpoints.
	 *
	 * @return the flatness of this curve.
	 */
	public double getFlatness() {
		return getFlatness(getX1(), getY1(), getCtrlX1(), getCtrlY1(),
				getCtrlX2(), getCtrlY2(), getX2(), getY2());
	}

	/**
	 * Returns the square of the flatness of this curve. The flatness is the
	 * maximum distance of a controlpoint from the line connecting the
	 * endpoints.
	 *
	 * @return the square of the flatness of this curve.
	 */
	public double getFlatnessSq() {
		return getFlatnessSq(getX1(), getY1(), getCtrlX1(), getCtrlY1(),
				getCtrlX2(), getCtrlY2(), getX2(), getY2());
	}

	/**
	 * Returns the start point.
	 *
	 * @return a <code>Point2D</code> that is the start point of the
	 *         <code>CubicCurve2D</code>.
	 */
	public abstract Point2D getP1();

	/**
	 * Returns the end point.
	 *
	 * @return a <code>Point2D</code> that is the end point of the
	 *         <code>CubicCurve2D</code>.
	 */
	public abstract Point2D getP2();

	/**
	 * Returns an iteration object that defines the boundary of the shape. The
	 * iterator for this class is not multi-threaded safe, which means that this
	 * <code>CubicCurve2D</code> class does not guarantee that modifications to
	 * the geometry of this <code>CubicCurve2D</code> object do not affect any
	 * iterations of that geometry that are already in process.
	 *
	 * @param at
	 *            an optional <code>AffineTransform</code> to be applied to the
	 *            coordinates as they are returned in the iteration, or
	 *            <code>null</code> if untransformed coordinates are desired
	 * @return the <code>PathIterator</code> object that returns the geometry of
	 *         the outline of this <code>CubicCurve2D</code>, one segment at a
	 *         time.
	 */
	public PathIterator getPathIterator(AffineTransform at) {
		return new CubicIterator(this, at);
	}
	/**
	 * Return an iteration object that defines the boundary of the flattened
	 * shape. The iterator for this class is not multi-threaded safe, which
	 * means that this <code>CubicCurve2D</code> class does not guarantee that
	 * modifications to the geometry of this <code>CubicCurve2D</code> object do
	 * not affect any iterations of that geometry that are already in process.
	 *
	 * @param at
	 *            an optional <code>AffineTransform</code> to be applied to the
	 *            coordinates as they are returned in the iteration, or
	 *            <code>null</code> if untransformed coordinates are desired
	 * @param flatness
	 *            the maximum amount that the control points for a given curve
	 *            can vary from colinear before a subdivided curve is replaced
	 *            by a straight line connecting the endpoints
	 * @return the <code>PathIterator</code> object that returns the geometry of
	 *         the outline of this <code>CubicCurve2D</code>, one segment at a
	 *         time.
	 */
	public PathIterator getPathIterator(AffineTransform at, double flatness) {
		return new FlatteningPathIterator(getPathIterator(at), flatness);
	}
	/**
	 * Returns the X coordinate of the start point in double precision.
	 *
	 * @return the X coordinate of the start point of the
	 *         <code>CubicCurve2D</code>.
	 */
	public abstract double getX1();
	/**
	 * Returns the X coordinate of the end point in double precision.
	 *
	 * @return the X coordinate of the end point of the
	 *         <code>CubicCurve2D</code>.
	 */
	public abstract double getX2();
	/**
	 * Returns the Y coordinate of the start point in double precision.
	 *
	 * @return the Y coordinate of the start point of the
	 *         <code>CubicCurve2D</code>.
	 */
	public abstract double getY1();

	/**
	 * Returns the Y coordinate of the end point in double precision.
	 *
	 * @return the Y coordinate of the end point of the
	 *         <code>CubicCurve2D</code>.
	 */
	public abstract double getY2();

	/**
	 * Tests if the shape intersects the interior of a specified set of
	 * rectangular coordinates.
	 *
	 * @param x
	 *            ,&nbsp;y the coordinates of the upper left corner of the
	 *            specified rectangular area
	 * @param w
	 *            the width of the specified rectangular area
	 * @param h
	 *            the height of the specified rectangular area
	 * @return <code>true</code> if the shape intersects the interior of the
	 *         specified rectangular area; <code>false</code> otherwise.
	 */
	public boolean intersects(double x, double y, double w, double h) {
		// Trivially reject non-existant rectangles
		if (w < 0 || h < 0) {
			return false;
		}

		// Trivially accept if either endpoint is inside the rectangle
		// (not on its border since it may end there and not go inside)
		// Record where they lie with respect to the rectangle.
		// -1 => left, 0 => inside, 1 => right
		double x1 = getX1();
		double y1 = getY1();
		int x1tag = getTag(x1, x, x + w);
		int y1tag = getTag(y1, y, y + h);
		if (x1tag == INSIDE && y1tag == INSIDE) {
			return true;
		}
		double x2 = getX2();
		double y2 = getY2();
		int x2tag = getTag(x2, x, x + w);
		int y2tag = getTag(y2, y, y + h);
		if (x2tag == INSIDE && y2tag == INSIDE) {
			return true;
		}

		double ctrlx1 = getCtrlX1();
		double ctrly1 = getCtrlY1();
		double ctrlx2 = getCtrlX2();
		double ctrly2 = getCtrlY2();
		int ctrlx1tag = getTag(ctrlx1, x, x + w);
		int ctrly1tag = getTag(ctrly1, y, y + h);
		int ctrlx2tag = getTag(ctrlx2, x, x + w);
		int ctrly2tag = getTag(ctrly2, y, y + h);

		// Trivially reject if all points are entirely to one side of
		// the rectangle.
		if (x1tag < INSIDE && x2tag < INSIDE && ctrlx1tag < INSIDE
				&& ctrlx2tag < INSIDE) {
			return false; // All points left
		}
		if (y1tag < INSIDE && y2tag < INSIDE && ctrly1tag < INSIDE
				&& ctrly2tag < INSIDE) {
			return false; // All points above
		}
		if (x1tag > INSIDE && x2tag > INSIDE && ctrlx1tag > INSIDE
				&& ctrlx2tag > INSIDE) {
			return false; // All points right
		}
		if (y1tag > INSIDE && y2tag > INSIDE && ctrly1tag > INSIDE
				&& ctrly2tag > INSIDE) {
			return false; // All points below
		}

		// Test for endpoints on the edge where either the segment
		// or the curve is headed "inwards" from them
		// Note: These tests are a superset of the fast endpoint tests
		// above and thus repeat those tests, but take more time
		// and cover more cases
		if (inwards(x1tag, x2tag, ctrlx1tag)
				&& inwards(y1tag, y2tag, ctrly1tag)) {
			// First endpoint on border with either edge moving inside
			return true;
		}
		if (inwards(x2tag, x1tag, ctrlx2tag)
				&& inwards(y2tag, y1tag, ctrly2tag)) {
			// Second endpoint on border with either edge moving inside
			return true;
		}

		// Trivially accept if endpoints span directly across the rectangle
		boolean xoverlap = (x1tag * x2tag <= 0);
		boolean yoverlap = (y1tag * y2tag <= 0);
		if (x1tag == INSIDE && x2tag == INSIDE && yoverlap) {
			return true;
		}
		if (y1tag == INSIDE && y2tag == INSIDE && xoverlap) {
			return true;
		}

		// We now know that both endpoints are outside the rectangle
		// but the 4 points are not all on one side of the rectangle.
		// Therefore the curve cannot be contained inside the rectangle,
		// but the rectangle might be contained inside the curve, or
		// the curve might intersect the boundary of the rectangle.

		double[] eqn = new double[4];
		double[] res = new double[4];
		if (!yoverlap) {
			// Both y coordinates for the closing segment are above or
			// below the rectangle which means that we can only intersect
			// if the curve crosses the top (or bottom) of the rectangle
			// in more than one place and if those crossing locations
			// span the horizontal range of the rectangle.
			fillEqn(eqn, (y1tag < INSIDE ? y : y + h), y1, ctrly1, ctrly2, y2);
			int num = solveCubic(eqn, res);
			num = evalCubic(res, num, true, true, null, x1, ctrlx1, ctrlx2, x2);
			// odd counts imply the crossing was out of [0,1] bounds
			// otherwise there is no way for that part of the curve to
			// "return" to meet its endpoint
			return (num == 2 && getTag(res[0], x, x + w)
					* getTag(res[1], x, x + w) <= 0);
		}

		// Y ranges overlap. Now we examine the X ranges
		if (!xoverlap) {
			// Both x coordinates for the closing segment are left of
			// or right of the rectangle which means that we can only
			// intersect if the curve crosses the left (or right) edge
			// of the rectangle in more than one place and if those
			// crossing locations span the vertical range of the rectangle.
			fillEqn(eqn, (x1tag < INSIDE ? x : x + w), x1, ctrlx1, ctrlx2, x2);
			int num = solveCubic(eqn, res);
			num = evalCubic(res, num, true, true, null, y1, ctrly1, ctrly2, y2);
			// odd counts imply the crossing was out of [0,1] bounds
			// otherwise there is no way for that part of the curve to
			// "return" to meet its endpoint
			return (num == 2 && getTag(res[0], y, y + h)
					* getTag(res[1], y, y + h) <= 0);
		}

		// The X and Y ranges of the endpoints overlap the X and Y
		// ranges of the rectangle, now find out how the endpoint
		// line segment intersects the Y range of the rectangle
		double dx = x2 - x1;
		double dy = y2 - y1;
		double k = y2 * x1 - x2 * y1;
		int c1tag, c2tag;
		if (y1tag == INSIDE) {
			c1tag = x1tag;
		} else {
			c1tag = getTag((k + dx * (y1tag < INSIDE ? y : y + h)) / dy, x, x
					+ w);
		}
		if (y2tag == INSIDE) {
			c2tag = x2tag;
		} else {
			c2tag = getTag((k + dx * (y2tag < INSIDE ? y : y + h)) / dy, x, x
					+ w);
		}
		// If the part of the line segment that intersects the Y range
		// of the rectangle crosses it horizontally - trivially accept
		if (c1tag * c2tag <= 0) {
			return true;
		}

		// Now we know that both the X and Y ranges intersect and that
		// the endpoint line segment does not directly cross the rectangle.
		//
		// We can almost treat this case like one of the cases above
		// where both endpoints are to one side, except that we may
		// get one or three intersections of the curve with the vertical
		// side of the rectangle. This is because the endpoint segment
		// accounts for the other intersection in an even pairing. Thus,
		// with the endpoint crossing we end up with 2 or 4 total crossings.
		//
		// (Remember there is overlap in both the X and Y ranges which
		// means that the segment itself must cross at least one vertical
		// edge of the rectangle - in particular, the "near vertical side"
		// - leaving an odd number of intersections for the curve.)
		//
		// Now we calculate the y tags of all the intersections on the
		// "near vertical side" of the rectangle. We will have one with
		// the endpoint segment, and one or three with the curve. If
		// any pair of those vertical intersections overlap the Y range
		// of the rectangle, we have an intersection. Otherwise, we don't.

		// c1tag = vertical intersection class of the endpoint segment
		//
		// Choose the y tag of the endpoint that was not on the same
		// side of the rectangle as the subsegment calculated above.
		// Note that we can "steal" the existing Y tag of that endpoint
		// since it will be provably the same as the vertical intersection.
		c1tag = ((c1tag * x1tag <= 0) ? y1tag : y2tag);

		// Now we have to calculate an array of solutions of the curve
		// with the "near vertical side" of the rectangle. Then we
		// need to sort the tags and do a pairwise range test to see
		// if either of the pairs of crossings spans the Y range of
		// the rectangle.
		//
		// Note that the c2tag can still tell us which vertical edge
		// to test against.
		fillEqn(eqn, (c2tag < INSIDE ? x : x + w), x1, ctrlx1, ctrlx2, x2);
		int num = solveCubic(eqn, res);
		num = evalCubic(res, num, true, true, null, y1, ctrly1, ctrly2, y2);

		// Now put all of the tags into a bucket and sort them. There
		// is an intersection iff one of the pairs of tags "spans" the
		// Y range of the rectangle.
		int tags[] = new int[num + 1];
		for (int i = 0; i < num; i++) {
			tags[i] = getTag(res[i], y, y + h);
		}
		tags[num] = c1tag;
		Arrays.sort(tags);
		return ((num >= 1 && tags[0] * tags[1] <= 0) || (num >= 3 && tags[2]
				* tags[3] <= 0));
	}

	/**
	 * Tests if the shape intersects the interior of a specified
	 * <code>Rectangle2D</code>.
	 *
	 * @param r
	 *            the specified <code>Rectangle2D</code> to be tested
	 * @return <code>true</code> if the shape intersects the interior of the
	 *         specified <code>Rectangle2D</code>; <code>false</code> otherwise.
	 */
	public boolean intersects(Rectangle2D r) {
		return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight());
	}

	/**
	 * Sets the location of the endpoints and controlpoints of this curve to the
	 * same as those in the specified <code>CubicCurve2D</code>.
	 *
	 * @param c
	 *            the specified <code>CubicCurve2D</code>
	 */
	public void setCurve(CubicCurve2D c) {
		setCurve(c.getX1(), c.getY1(), c.getCtrlX1(), c.getCtrlY1(), c
				.getCtrlX2(), c.getCtrlY2(), c.getX2(), c.getY2());
	}

	/**
	 * Sets the location of the endpoints and controlpoints of this curve to the
	 * specified double coordinates.
	 *
	 * @param x1
	 *            ,&nbsp;y1 the first specified coordinates used to set the
	 *            start point of this <code>CubicCurve2D</code>
	 * @param ctrlx1
	 *            ,&nbsp;ctrly1 the second specified coordinates used to set the
	 *            first control point of this <code>CubicCurve2D</code>
	 * @param ctrlx2
	 *            ,&nbsp;ctrly2 the third specified coordinates used to set the
	 *            second control point of this <code>CubicCurve2D</code>
	 * @param x2
	 *            ,&nbsp;y2 the fourth specified coordinates used to set the end
	 *            point of this <code>CubicCurve2D</code>
	 */
	public abstract void setCurve(double x1, double y1, double ctrlx1,
			double ctrly1, double ctrlx2, double ctrly2, double x2, double y2);

	/**
	 * Sets the location of the endpoints and controlpoints of this curve to the
	 * double coordinates at the specified offset in the specified array.
	 *
	 * @param coords
	 *            a double array containing coordinates
	 * @param offset
	 *            the index of <code>coords</code> at which to begin setting the
	 *            endpoints and controlpoints of this curve to the coordinates
	 *            contained in <code>coords</code>
	 */
	public void setCurve(double[] coords, int offset) {
		setCurve(coords[offset + 0], coords[offset + 1], coords[offset + 2],
				coords[offset + 3], coords[offset + 4], coords[offset + 5],
				coords[offset + 6], coords[offset + 7]);
	}

	/**
	 * Sets the location of the endpoints and controlpoints of this curve to the
	 * specified <code>Point2D</code> coordinates.
	 *
	 * @param p1
	 *            the first specified <code>Point2D</code> used to set the start
	 *            point of this curve
	 * @param cp1
	 *            the second specified <code>Point2D</code> used to set the
	 *            first control point of this curve
	 * @param cp2
	 *            the third specified <code>Point2D</code> used to set the
	 *            second control point of this curve
	 * @param p2
	 *            the fourth specified <code>Point2D</code> used to set the end
	 *            point of this curve
	 */
	public void setCurve(Point2D p1, Point2D cp1, Point2D cp2, Point2D p2) {
		setCurve(p1.getX(), p1.getY(), cp1.getX(), cp1.getY(), cp2.getX(), cp2
				.getY(), p2.getX(), p2.getY());
	}

	/**
	 * Sets the location of the endpoints and controlpoints of this curve to the
	 * coordinates of the <code>Point2D</code> objects at the specified offset
	 * in the specified array.
	 *
	 * @param pts
	 *            an array of <code>Point2D</code> objects
	 * @param offset
	 *            the index of <code>pts</code> at which to begin setting the
	 *            endpoints and controlpoints of this curve to the points
	 *            contained in <code>pts</code>
	 */
	public void setCurve(Point2D[] pts, int offset) {
		setCurve(pts[offset + 0].getX(), pts[offset + 0].getY(),
				pts[offset + 1].getX(), pts[offset + 1].getY(), pts[offset + 2]
						.getX(), pts[offset + 2].getY(),
				pts[offset + 3].getX(), pts[offset + 3].getY());
	}

	/**
	 * Subdivides this cubic curve and stores the resulting two subdivided
	 * curves into the left and right curve parameters. Either or both of the
	 * left and right objects may be the same as this object or null.
	 *
	 * @param left
	 *            the cubic curve object for storing for the left or first half
	 *            of the subdivided curve
	 * @param right
	 *            the cubic curve object for storing for the right or second
	 *            half of the subdivided curve
	 */
	public void subdivide(CubicCurve2D left, CubicCurve2D right) {
		subdivide(this, left, right);
	}

}
